Question

using euclid's algorithm to find HCF of 1190 and 1445 Express the HCF in the form of 1119m+1445n.

Answer 1

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Answer 2

Answer:

HCF of 1190 and 1445 is 85.

Step-by-step explanation:

Given two numbers 1190 and 1445. we have to find the HCF by euclid's algorithm.

Euclid algorithm lemma, a = bq + r where 0 ≤ r < b

1445 = 1190 × 1 + 255 →  (1)

1190 = 255 × 4 + 170   →   (2)

255 = 170 × 1 + 85

170 = 85 × 2 + 0

Hence, HCF i.e highest common factor is 85

Now, 85 = 255 - 170 [ from ( 1 ) ]

 = [1445 - (1190 × 1)] - [1190 - (255 × 4)]

 = 1445 - 1190 - 1190 + (255 × 4)

             = 1445 - (2 × 1190) + (1445 - (1190 × 1)) × 4   [ from ( 1 ) ]

 = 1445 - (2 × 1190) + (4 × 1445) - (4 × 1190)

= 1190 ( - 6 ) + 1445 ( 5 )

Compare with HCF = 1190m + 1445n

we get, m = - 6 and n = 5